Transient behaviour of magnetic micro-bead chains rotating in a fluid by external fields

Abstract

Magnetic micro-beads can facilitate many functions in lab-on-a-chip systems, such as bio-chemical labeling, selective transport, magnetic sensing and mixing. In order to investigate potential applications of magnetic micro-beads for mixing in micro fluidic systems, we developed a pin-jointed mechanism model that allows analysing the behaviour of rotating superparamagnetic bead chains. Our numerical model revealed the response of the chains on a rotating magnetic field over time. We could demonstrate that the governing parameters are the Mason number and number of beads in the chain. The results are in agreement with the simplified analytical model, assuming a straight chain, but also allow prediction of the transient chain shape. The modelled chains develop an anti-symmetric S-shape that is stable, if the Mason number for a given chain length does not surpass a critical value. Above that value, rupture occurs in the vicinity of the chain centre. However, variations in bead susceptibility can shift the location of rupture. Moreover, we performed experiments with superparamagnetic micro-beads in a small fluid volume exposed to a uniform rotating magnetic field. Our simulation could successfully predict the observed transient chain form and the time for chain rupture. The developed model can be used to design optimised bead based mixers in micro fluidic systems.

Resistive pulse sensing of magnetic beads and supraparticle structures using tunable pores

“…pore constriction. This observation is consistent with previous observations of chains breaking in shear flows, 56 and a similar scaling argument can be applied here, by considering the hydrodynamic (F h ) and magnetic (F m ) forces between the two spheres. F h can be estimated using…”

“…41,[47][48][49][50] Precise application of magnetic fields has enabled device-based quadrupole sorting, [51][52][53][54] active bead transport for biosensing, 55 and dynamic manipulation of magnetic supraparticle structures (SPSs). 56 For applications in which target analytes contain multiple binding sites or epitopes, it is possible for the target to bind to multiple beads simultaneously, leading to aggregation. 41,[57][58][59] Multiple-particle binding has been used in LM, allowing detection of the dengue virus at 10 plaque forming units ml À1 .…”

Dynamics of magnetic chains in a shear flow under the influence of a uniform magnetic field

“…In such applications, magnetic particles are adopted as mobile substrates for bio-assays, stirring agents to achieve efficient mixing, or actuators. [3][4][5][6][7][8][9][10] Under typical operating conditions, due to small length scale, flows in these devices are laminar and inertia of both fluid and particles may be neglected.…”

“…In many previous studies, the particle dynamics method based on the point-dipole approximation and the Stokes drag law has been extensively employed due to its simplicity. 9,11,15,17 However, this method may lead to quantitatively inaccurate results in the cases with closely packed particles like clusters or chains. More sophisticated numerical schemes based on the Stokesian dynamics are capable of treating multi-body hydrodynamic interactions, but still with an approximation on the magnetic forces.…”

Flexible mechanism of magnetic microbeads chains in an oscillating field

“…These two fields had comparable amplitudes, which resulted in an overall oscillating field H 0 = H x i + H y j, where i and j are unit vectors in the directional and perpendicular axes, respectively. For this type of oscillating field configuration, the phase angle trajectory (θ) of the external field is expressed as θ(t) = tan -1 To determine the critical local Mason number, which dominates the deformation and structural instability of the chain, a pin-jointed mechanism 23 depicted in figure 1 is employed to define local phase lag (∆θ Li ) between dyad of beads and overall field for an oscillating bending chain. A dyad can be regarded as the basic structural unit of the chain and the bar is utilized to determine the local phase angle trajectory (θ i ) and the local phase lag (∆θ Li ).…”